Recursive Kinematic Propagation for Wheeled Mobile Robots

Abstract

The problem of wheeled mobile robot kinematics is formulated using the transport theorem of vector algebra. Doing so postpones the introduction of coordinates until after the expressions for the relevant Jacobians have been derived. This approach simplifies the derivation while also providing the solution to the general case in 3D, including motion over rolling terrain. Angular velocity remains explicit rather than encoded as the time derivative of a rotation matrix. The equations are derived and can be implemented recursively using a single equation that applies to all cases. Acceleration kinematics are uniquely derivable in reasonable effort. The recursive formulation also leads to efficient computer implementations that reflect the modularity of real mechanisms.